Ending the Pacific War quickly, bringing the Japanese to the negotiating table - these are the usual arguments. The Japanese were themselves close to chaos, which is a further reason they had not agreed an end to the fighting. They couldn't agree among themselves.
Other reasons..? To show the Russians - to effectively start what became the Cold War. To test in a real situation, the new 'toy' that Oppenheimer had made. Each B29 with a bomb had 4 or 5 other B29's with it - of these, 1 was for photography, 1 was for measurements.
https://en.wikipedia.org/wiki/Atomic_bombings_of_Hiroshima_and_Nagasaki#Hiroshima
Why did they drop the 2nd bomb..? Well, the Japanese had not responded after the first one. But the 2nd one was a different type - it was the design they had tested, in the desert - the Fat Man. Cynically, I might suggest it was another toy.
Some quotes, from Robert Oppenheimer, who lead the Manhattan Project:
http://www.brainyquote.com/quotes/authors/j/j_robert_oppenheimer.html
It cannot be un-created. This Genie is out of its Bottle.
The nightmare for us all, is a 'rogue' state, who
is prepared to unleash one again.
I
